🪐 2D Laplace Resonance of Io, Europa and Ganymede: Libration of the Resonant Angle, Conjunctions and Tidal Heating

What It Demonstrates

A genuine three-body mean-motion resonance: the Laplace angle phi = lambda_Io - 3 lambda_Europa + 2 lambda_Ganymede stays bounded near 180 degrees (it librates) instead of drifting through all values, and n_Io - 3 n_Europa + 2 n_Ganymede is zero. The in-page checks measure the synodic period, the 90 degree offset of Ganymede at Io-Europa conjunctions and the 2071-day libration period.

How to Use

Pick a preset, press the Libration speed button and watch the gauge and the Laplace-angle graph. Use the libration kick, the Ganymede mean-motion offset, moon masses and J2 sliders to see when the lock holds and when the angle starts to circulate.

Did You Know?

Io, Europa and Ganymede can never all line up on the same side of Jupiter: when Io and Europa are in conjunction Ganymede is about 90 degrees away, and when Europa and Ganymede are in conjunction Io is on the opposite side. The resonance keeps their orbits slightly eccentric, which makes tides flex Io about 1e14 W worth, the reason it is the most volcanic body in the Solar System.